报 告 人: 王兆军 教授
南开大学 博士生导师
报告题目:Nonparametric Maximum Likelihood Approach to Multiple Change-Point Problems
报告时间:
报告地点:静远楼1508会议室
主办单位:太阳成集团、科技处
南开大学数学科学学院副院长,博士生导师。1990年7月于华东师范大学统计系毕业并获得硕士学位,1995年12月于南开大学数学科学学院毕业并获得博士学位。2000年晋升为教授,2001年被聘为博士生导师,共培养硕士研究生30多名,博士研究生10多名,其中两人获教育部学术新人奖,两人获南开大学宝钢特等奖,两人获“南开十杰”称号,一人获全国百篇优秀博士学位论文,一人博士论文于2012年被国家统计局评为全国统
报告摘要:
In multiple change-point problems, different data segments follow different distributions where changes may be in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated by using the dynamic programming algorithm and further taking advantage of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation for both the locations and magnitudes of the change-points with a rate, $(\log n)^2$, where $n$ is the sample size. We also suggest a pre-screening procedure which is capable of excluding most of the irrelevant points. Simulation studies show that the proposed method has outstanding performance of identifying multiple change-points in terms of estimation accuracy and computation time compared with existing methods. The new methodology is illustrated with two real data examples.